TY - JOUR

T1 - Emergence of spontaneous symmetry breaking in dissipative lattice systems

AU - Wilming, Henrik

AU - Kastoryano, Michael J.

AU - Werner, Albert H.

AU - Eisert, Jens

N1 - Funding Information: This work has been supported by the ERC (TAQ), the EU (RAQUEL, AQuS, SIQS), the COST network, the DFG (Grant Nos. CRC 183 and EI 519/7-1), and the Studienstiftung des Deutschen Volkes. M.J.K. was supported by the Carlsberg foundation and the Villum foundation.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.

AB - A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.

UR - http://www.scopus.com/inward/record.url?scp=85016164404&partnerID=8YFLogxK

U2 - 10.1063/1.4978328

DO - 10.1063/1.4978328

M3 - Article

AN - SCOPUS:85016164404

VL - 58

JO - Journal of mathematical physics

JF - Journal of mathematical physics

SN - 0022-2488

IS - 3

M1 - 033302

ER -